Audio line receiver impedance balancing using a 2nd diff amp

The single op-amp differential amplifier shown in Figure 1 is often used as an audio balanced line receiver. Obtaining high common-mode rejection is a critical requirement that requires four highly-matched resistors.

Audio line receiver ICs, with laser trimmed on-chip resistors (such as the unity-gain THAT1240/INA134 or "-6dB" attenuating THAT1246/INA137) have excellent common-mode rejection, typically 90 dB. Real world audio interconnections are not always balanced and are frequently a combination of unbalanced single-ended, balanced, floating and ground-referred sources.

The simple differential amplifier topology of Figure 1, whether made from op amps using external precision resistors or readily-available line receiver ICs, has two subtle limitations that prevent it from being truly universal.

Simple diff amps have unpredictable input impedance and gain
The first limitation is the unpredictable input "port" impedances to ground at each input. The impedance at the inverting (-) input is voltage-dependent on the non-inverting (+) input. Depending on the type of connections to the inputs, (e.g., unbalanced single-ended, balanced ground-referred, or fully-floating) the apparent impedance at the inverting input can vary over a wide range. An extreme example is when a grounded center-tap transformer drives both inputs with equal but opposite polarities.

In a unity-gain line receiver (where R1=R2=R3=R4) the signal current in the inverting input is three times the non-inverting input current [1,2,3]. Fortunately, the impedance for common-mode signals (both inputs driven equally) are identical at each input port or the circuit in Figure 1 would perform poorly when rejecting hum and interference in the real world.

A second limitation is unequal gain when fed by single-ended sources that have one input connected and the other left floating or "open port." Typical open-port examples are a three--conductor 1/4" (TRS) plug with the "ring" terminal unconnected or an XLR to RCA phono plug adapter cable with either pin 2 or 3 open. In Figures 2a and 2b, a unity-gain line receiver is shown.

Figure 2: Gain variations occur using the circuit of Figure 1 when one input is driven and the opposing input is "open port." Figures 2a and 2b show unity-gain line receivers; 2c and 2d are -6dB examples.

Driving the inverting input while leaving the non-inverting input open provides the expected gain of 0 dB. However, reversing the input connections (feeding the non-inverting input with the inverting input open) provides 6dB attenuation because there is no ground connection for the inverting feedback network to provide 6 dB of gain to negate identical attenuation at the non-inverting input.

In professional audio applications an "impedance-balanced" input having an equal and consistent input impedance to ground regardless of how it's being driven is desirable [1,2,3]. When fed by single-ended sources, a line receiver having predictable gain regardless of which input port is used, and whether the opposing input is open or "closed" (connected), is also a worthwhile property.

The "Brand-Rex" cable I have measured is undocumented and I haven't measured resistance or inductance per foot.
I do have the published specs for Belden 9451 which is quite similar posted here: http://www.ka-electronics.com/images/jpg/Belden_9451_Signal_Characteristics.jpg
It shows 0.17 uH per foot and 14.1 Ohms per 1000 feet for the conductors.

"But doesn't not grounding at both ends leave the system open to EMI issues?"
Please refer to Muncy "Noise Susceptibility in Analog and Digital Signal Processing Systems" http://www.aes.org/e-lib/browse.cfm?elib=7945
And Whitlock "Common-Mode to Differential-Mode Conversion in Shielded Twisted-pair Cables (Shield-Current-Induced Noise)" http://www.aes.org/e-lib/browse.cfm?elib=12594
As well as Whitlock's "Balanced Lines in Audio Systems: Fact, Fiction, and Transformers" http://www.aes.org/e-lib/browse.cfm?elib=7944
"If you use that circuit you linked to earlier, that uses a 1MOhm to gnd T-network, then does that get you enough CMRR?"
It depends on the source impedance imbalance (not the shunt capacitance to ground if the shield is grounded at the source) and how much CMRR is enough. Do realize that the 1M Ohm could be made larger (e.g. 4M7) approaching the CM impedance of InGenius bootstrapped approaches. The value is primarily limited by the op-amp bias current and the allowable reduction in DC common mode range. For an LME49860 with a worst-case I bias of 72 nA per input, the maximum CM Vos that would develop is approx. 680 mV. Typically at 10 nA per input it would be less than 100 mV. This CM Vos is rejected by the following diff amp and the Inoise that develops across it also appears in common mode.
"Thinking the difference amp that follows the buffers can be anything you want, like good old INAxxx."
Yes it could be an INA134/137 THAT1240/1246 or be cross-coupled (INA2137/THAT1286) to provide a differential output. Alternatively a conventional op amp and precision resistors could be used to lower the circuit impedances and Johnson noise though the resulting CMRR - and the noise performance with a high value of Rcm - might not be as good due to resistor mis-match.

But doesn't not grounding at both ends leave the system open to EMI issues?
Interesting info on the capacitive imbalance over 1km. At 1kHz, the imbalance in the two impedances to gnd is about 277Ohms. If you use that circuit you linked to earlier, that uses a 1MOhm to gnd T-network, then does that get you emough CMRR? Thinking the difference amp that follows the buffers can be anything you want, like good old INAxxx.

Bill Whitlock points out in Ballou "Handbook for Sound Engineers" 4th ed. that by grounding the driven end shield, and not the receiving end, common mode to differential conversion at the receiver due to capacitive imbalance from the cable is avoided.

"The reason I singled out cable Z imbalance is because of the capacitance to ground variation of each wire in the cable. I'm thinking about impedance mismatch over frequency, not at dc."
Over long runs the capacitance to shield variations are significant. As a point of reference I measured approx. 1000 feet of "8451-type" two conductor foil shield with drain wire cable and found that the conductors measured 40.9 nF vs. 43.8 nF.

"I'm aware of the CM i/p Z problem of conventional audio difference amps and how the system CMR gets blatted by cable Z mismatch."
Yes the effect is well documented though I think you may mean source Z mis-match which also includes the cable as well as what is driving it.
What I've never seen in the wild however is an audio tieline that develops (say 20 Ohms) resistive imbalance. I've cleaned a lot of dirty patchbays and cords in my career and replaced switches that may have developed 20 Ohms or more imbalance, or fixed a bad Elco or "DL" connector pin but I was never called to fix it because it hummed due to reduced CM. The call or note from the engineer was that the patchcord or switch sounded "crunchy" or the circuit was open.
I'm also not sure how a "proper" balanced output could develop a 20 Ohm imbalance. Typical build-out resistors might be 47R 1% and have at most a 1 Ohm error. One would have to use 1K build-outs with 1% resistors to approach 20R imbalance.
So my question is how do we arrive at such large imbalances? I realize that with 9-25K Zcm inputs 1 Ohm imbalance is significant but it generally doesn't produce session-stopping hum.
"Can you explain the shortcomings of using e.g. INA317, its inputs buffered by 2 x op-amp stages like OPA1642 (to make a classic instrumentation amp), plus say 4.7MOhm resistors to gnd on each op-amp input for bias?"
I'll let Bill take that question. The circuit you propose is similar overall to this one only the linked citation refers to a bipolar op-amp with T-bias and AC-coupling. It's a simplified circuit:
http://www.proaudiodesignforum.com/forum/php/viewtopic.php?f=6&t=557
There's a lot of flexibility in the value choice of input T-bias values and Cin. As shown, the differential -3dB point is 4 Hz. For common mode signals the LF cutoff is approximately 0.1 Hz.

"The i-related voltage noises in R1 and R2 will not be nullified by the following diff-amp."
Correct. That's why their values are relatively low.
"The two i-noises will add as the sq-rt of the sum of their squares in R7, creating a common-mode noise component that will be nullified in the diff-amp."
Also correct. That's why it's magic. Should also point out to our readers that a DC-term develops there also in common mode and is nulled out. For the THAT151X and NE5532 examples if Rcm is made too large there will be a reduction in headroom. That sets the upper limit. For a 5532 with a Ibias per input max of 1500nA, 3 uA total, a 1M can produce a Vcm of 3V. An LME49860, with an Ibias per input of 72 nA max (144 nA total) the Vcm with a 1M is less than 150mV.
I prefer to use the "T-bias" approach (and InGenius) with AC-coupled inputs to provide great LF CM because it reduces capacitor matching requirements considerably.
"Even if just two high-value resistors to ground supplied bias, I doubt they'd contribute significant noise because it will be seriously attenuated by the differential source impedance - somewhere in the 150 to 200 ohm range for a mic preamp."
In a mic preamp with coupling capacitors you'll never see a 150-200 source impedance at LF which gives rise to 1/f noise. At 20Hz 22uF (~47uF/2)you'll see an added 360 Ohms to the 150-200R source Z from capacitor reactance. Thus, in a preamp R1 and R2 still need to be kept relatively low.